Integrated Decisions for Supply Chain Design and Inventory Allocation Problem

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Mangotra, Divya
Lu, Jye-Chyi
Al-Khayyal, Faiz
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Manufacturing outsourcing in the U.S. has never been stronger than it is today. Increased outsourcing has led to significant changes in the design of the retail distribution network. While the traditional distribution network had the manufacturing plants supplying goods to the retail stores directly, the off-shore manufacturing has increased the network's demand for transportation and warehousing to deliver the goods. Thus, most companies have a complex distribution network with several import and regional distribution centers (RDC). In this thesis, we study an integrated facility location and inventory allocation problem for designing a distribution network with multiple national (import) distribution centers (NDC) and retailers. The key decisions are where to locate the RDCs and how much inventory to hold at the different locations such that the total network cost is minimized under a pre-defined operational rule for the distribution of goods. In particular, the inventory cost analysis is based on the continuous review batch ordering policy and the base-stock policy. Both Type-I (probability of stock-outs) and Type-II (fill-rate) service level measures are used in the analysis. Two different models are presented in this thesis for solving the integrated facility location-inventory allocation problem. The first model, continuous approximation (CA), assumes the distribution network to be located in a continuous region and replaces the discrete store locations with a store density function. The second model is a discrete representation of the problem as a mixed integer programming problem. Both the models take a nonlinear form and solution techniques are developed using the theory of nonlinear programming and linear reformulation of nonlinear problems. The goal of the first part of the thesis is to model the problem using a modified CA approach and an iterative solution scheme is presented to solve it. The main contribution of this work lies in developing a refined CA modeling technique when the discrete data cannot be modeled by a continuous function. In addition, the numerical analysis suggests that the total network cost is significantly lower in the case of the integrated model as compared with the non-integrated model. It is also shown that the regular CA approach leads to a solution which is inferior to the solution obtained by the modified CA approach. Our analysis shows that the type of service measure used affects the network design. In the second part of the thesis, the problem is modeled as a nonlinear mixed integer program and a linear reformulation solution technique is proposed to obtain a lower bound on the original problem. Computational results are presented for small problem instances. We conclude this part of the thesis by presenting an integrated model when a base stock inventory policy is used. A drop-decomposition heuristic is proposed to solve this problem.
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